a(n) = Sum_{k=0..n} T(n,n+k), T given by A027023.

Terms

a(0) =1a(1) =2a(2) =5a(3) =14a(4) =39a(5) =112a(6) =323a(7) =932a(8) =2693a(9) =7790a(10) =22565a(11) =65466a(12) =190243a(13) =553748a(14) =1614363a(15) =4713432a(16) =13780841a(17) =40343210a(18) =118243273a(19) =346937614a(20) =1018958151a(21) =2995407840a(22) =8812890391a(23) =25948662684a(24) =76457517949a(25) =225429675606a(26) =665069604713